Discriminative Face Recognition Methods with Structure and Label Information via \(l_2\)-Norm Regularization

Existing sparse representation methods either fail to incorporate the structure and label information of training samples, or suffer from expensive computation for \(l_1\)- or \(l_{2,1}\)-norm. In this paper, we propose three discriminative sparse representation classification methods with structure and label information based on \(l_2\)-norm regularization for robust face recognition. We propose the first classification method with structure and label information by enforcing competition among the representation results of training samples from different classes in representing a test sample. To make the classification more discriminative, we present the decorrelation classification method with structure and label information by jointly considering the competition and decorrelation regularizations. In addition, by incorporating the locality information of samples, we propose the third method called locality-constrained decorrelation classification method with structure and label information. The proposed methods not only contain the structure and label information of training samples, but also have low computational cost owing to the use of \(l_2\)-norm. All three methods have closed-form solutions, rendering them easy to solve and calculate efficiently. Importantly, the proposed methods can achieve better recognition results than most existing state-of-the-art sparse representation methods. Furthermore, based on the proposed methods, we illustrate the effect of different regularization constraints on the recognition performance. Experiments on the ORL, Extended YaleB, FERET, and LFW databases validate the effectiveness of the proposed methods.